mysql 相关子查询 where 和 group by

如何解决mysql 相关子查询 where 和 group by

这是我的相关子查询，我的 group by 子句是不必要的吗？

SELECT product_type,product_name,sale_price
  FROM product AS p1
 WHERE sale_price > (SELECT AVG(sale_price)
                       FROM product AS p2
                      WHERE p1.product_type = p2.product_type
                      GROUP BY product_type);